Simplify (3x)/(5(x+y))-(2y)/(3(x+y))

$\frac{3 x}{5 (x + y)} - \frac{2 y}{3 (x + y)}$

To write $\frac{3 x}{5 (x + y)}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{5 (x + y)} \cdot \frac{3}{3} - \frac{2 y}{3 (x + y)}$

To write $- \frac{2 y}{3 (x + y)}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x}{5 (x + y)} \cdot \frac{3}{3} - \frac{2 y}{3 (x + y)} \cdot \frac{5}{5}$

Write each expression with a common denominator of $15 (x + y)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{5 (x + y)}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 3}{5 (x + y) \cdot 3} - \frac{2 y}{3 (x + y)} \cdot \frac{5}{5}$

Multiply $3$ by $5$ .

$\frac{3 x \cdot 3}{15 (x + y)} - \frac{2 y}{3 (x + y)} \cdot \frac{5}{5}$

Multiply $\frac{2 y}{3 (x + y)}$ by $\frac{5}{5}$ .

$\frac{3 x \cdot 3}{15 (x + y)} - \frac{2 y \cdot 5}{3 (x + y) \cdot 5}$

Multiply $5$ by $3$ .

$\frac{3 x \cdot 3}{15 (x + y)} - \frac{2 y \cdot 5}{15 (x + y)}$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 - 2 y \cdot 5}{15 (x + y)}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{9 x - 2 y \cdot 5}{15 (x + y)}$

Multiply $5$ by $- 2$ .

$\frac{9 x - 10 y}{15 (x + y)}$